How to set all selected vertices to height of another vertex?
One way to do this is to set the pivot point for transforms to be the active element, by choosing Active Element for the Pivot Point in the bar below the 3D View:



If you have Pie Menus enabled, you can press .>7 instead.

Then select all the vertices you want to affect making sure that the one whose height you want to copy is the active one (i.e. select it last) and just Scale in the Z axis direction to 0, by pressing S, then Z and then 0.